Exploratory Analysis: Clustering of the PCA scores

In order to find similar behavior and patterns in the data, the principal component scores derived from univariate FPCAs for each scenario and each PFT are clustered with a 4-means algorithm. The data used to cluster consists of 10 PC scores - the first two components for each of the five PFTs. The resulting four clusters are rather unbalanced as the table above indicates:

Number of curves in each cluster
Control SSP1-RCP2.6 SSP3-RCP7.0 SSP5-RCP8.5
Cluster 1 99 99 147 64
Cluster 2 161 95 203 244
Cluster 3 90 87 35 115
Cluster 4 84 161 77 42

Interestingly, the two most drastic scenarios are dominated by two large clusters, while the scenarios Control and SSP1-RCP2.6 are more balanced with only one dominating cluster.

In the following, for each PFT the four clusters are portrayed.

Clusters - PFT Tundra

At first, let’s take a look at PFT Tundra. Figure 1 shows the first two principal components plotted against each other for each scenario, colors are indicating the cluster.

Figure 1: PC 1 vs. PC 2 for Tundra and all four scenarios.
Figure 1: PC 1 vs. PC 2 for Tundra and all four scenarios.

The clustering is slightly detectable but the visual clusters are not met entirely.

Figure 2 shows the clustered curves for scenario Control for each cluster. The color indicates the cluster and the dark curves represent the mean functions.

Figure 2: Clustered curves for scenario Control and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 2: Clustered curves for scenario Control and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

We can see clearly some grouping structure here: cluster 4 represent all the grid cells with a high share of Tundra throughout the whole time period while cluster 2 represents those curves with a rather high peak. The differences between the other two clusters are less pronounced.

Figure 3 shows the equivalent plot for scenario SSP1-RCP2.6:

Figure 3: Clustered curves for scenario SSP1-RCP2.6 and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 3: Clustered curves for scenario SSP1-RCP2.6 and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Here, cluster 2 reflects (among others) grid cells with a lower peak in share of above ground carbon than the other three clusters. Besides that, no clear patterns are visible. For scenario SSP3-RCP7.0 in Figure 4, another pattern is present in the clusters: cluster 3 represents those grid cells with a sharp decrease in portion, while cluster 1 represents the opposite. The two other clusters mainly focus on the height of the peak.

Figure 4: Clustered curves for scenario SSP3-RCP7.0 and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 4: Clustered curves for scenario SSP3-RCP7.0 and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Finally, Figure 5 shows the clustering for scenario SSP5-RCP8.5. The patterns are pretty similar with cluster 4 representing the sharpest decreases. Note that only clusters 1 and 4 represent the grid cells with lower peak.

Figure 5: Clustered curves for scenario SSP5-RCP8.5 and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 5: Clustered curves for scenario SSP5-RCP8.5 and PFT Tundra. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

In total, for Tundra, there is a light grouping detectable in the data.

Clusters - Needleleaf Evergreen

Now, let’s take a look at PFT Needleleaf Evergreen. Figure 6 shows the first two principal components plotted against each other:

Figure 6: PC 1 vs. PC 2 for Needleleaf Evergreen and all four scenarios.
Figure 6: PC 1 vs. PC 2 for Needleleaf Evergreen and all four scenarios.

In contrast to Tundra, now the clustering is clearly visible. The more drastic the warming scenario, the less overlap exist among the clusters.

Figure 7 shows the clustering for the Control scenario. Here, the clustering is clearly present: Cluster 2 represents grid cells with a rather high share of Needleleaf Evergreen, while cluster 1 represents grid cells with low shares. The third and forth cluster cover the functions in between.

Figure 7: Clustered curves for scenario Control and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 7: Clustered curves for scenario Control and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Figure 8 shows the equivalent plot for scenario SSP1-RCP2.6. Here, the grouping structure is even more apparent: the dominating cluster 4 represents curves with a high share of Needleleaf Evergreen, while clusters 1, 2 and 3 represent grid cells with a low to mediate share.

Figure 8: Clustered curves for scenario SSP1-RCP2.6 and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 8: Clustered curves for scenario SSP1-RCP2.6 and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

In Figure 9, the same pattern in visible for scenario SSP3-RCP7.0, with clusters 2, 3 and 4 representing low shares and cluster 1 those with high shares.

Figure 9: Clustered curves for scenario SSP3-RCP7.0 and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 9: Clustered curves for scenario SSP3-RCP7.0 and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Finally, Figure 10 shows the equivalent plot for scenario SSP5-RCP8.5. Again, the one of the dominating clusters (cluster 3) represent high shares of above ground carbon while cluster 1, 2 and 4 represent low shares.

Figure 10: Clustered curves for scenario SSP5-RCP8.5 and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 10: Clustered curves for scenario SSP5-RCP8.5 and PFT Needleleaf Evergreen. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

In summary, the clusters a highly driven by the share of Needleleaf Evergreen. See the summary at the end of this document for a detailed description.

Clusters - Pioneering Broadleaf

Figure 11 shows a plot of the first two principal components for each scenario. Again, a clear grouping is present in the data.

Figure 11: PC 1 vs. PC 2 for Pioneering Broadleaf and all four scenarios.
Figure 11: PC 1 vs. PC 2 for Pioneering Broadleaf and all four scenarios.

Figure 12 shows the clustered curves for scenario Control. Cluster 1 is driven by grid cells with a (very) high share of Pioneering Broadleaf. Cluster 2 and 4 cover all grid cells with rather low shares, the mean functions hardly vary from zero. Cluster 3 represents all functions in between.

Figure 12: Clustered curves for scenario Control and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 12: Clustered curves for scenario Control and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Figure 13 shows the equivalent plot for scenario SSP1-RCP2.6. Here, two clusters represent high shares (cluster 1 and 4), while cluster 2 reflects mediate shares of above ground carbon. The dominating cluster 4 covers all grid cells with a very low share of Pioneering Broadleaf.

Figure 13: Clustered curves for scenario SSP1-RCP2.6 and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 13: Clustered curves for scenario SSP1-RCP2.6 and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

For scenario SSP3-RCP7.0 depicted in Figure 14, cluster 2 and 4 represent grid cells with a high share of above ground carbon, but at other time points: cluster 4 covers those with a less steep increase. Cluster 1 reflects curves which are near zero for most of the time span and cluster 3 covers thise with a mediate peak in the beginning and a fast decrease afterwards.

Figure 14: Clustered curves for scenario SSP3-RCP7.0 and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 14: Clustered curves for scenario SSP3-RCP7.0 and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Also for the most drastic scenario SSP5-RCP8.5 depicted in Figure 15, the same pattern is present: now, clusters 1 and 2 represent high shares while clusters 3 and 4 reflect lower shares. Similar to above, cluster 4 covers the curves with a peak in ethe beginning of the study period, while cluster three covers those with a peak in the later years.

Figure 15: Clustered curves for scenario SSP5-RCP8.5 and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 15: Clustered curves for scenario SSP5-RCP8.5 and PFT Pioneering Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

In total, the clusters are very much affected by PFT Pioneering Broadleaf.

Clusters - other Conifers

As for the other PFTs, Figure 16 shows the first two principal components plotted against each other for each scenario. Similar to Tundra, the grouping structure is less clear, but still visible.

Figure 16: PC 1 vs. PC 2 for other Conifers and all four scenarios.
Figure 16: PC 1 vs. PC 2 for other Conifers and all four scenarios.

Figure 17 shows the clustered curves for scenario Control. Cluster 3 represents the grid cells with a high share of above ground carbon, while the other three clusters - looking at the mean functions - mainly differ in terms of the peak.

Figure 17: Clustered curves for scenario Control and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 17: Clustered curves for scenario Control and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

For scenario SSP1-RCP2.7 depicted in Figure 18 another pattern is apparent: cluster 4 reflects higher shares of other Conifers, while cluster 1 and 3 cover those grid cells with a small peak in the beginning of the time span.

Figure 18: Clustered curves for scenario SSP1-RCP2.6 and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 18: Clustered curves for scenario SSP1-RCP2.6 and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Figure 19 shows the equivalent plot for scenario SSP3-RCP7.0. Again, one cluster represents higher shares (cluster 1), while clusters 2 and 3 represent those curves with a peak in the beginning.

Figure 19: Clustered curves for scenario SSP3-RCP7.0 and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 19: Clustered curves for scenario SSP3-RCP7.0 and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

And the same holds true for the most drastic scenario SSP5-RCP8.5 visualized in Figure 20, now with clusters 2 and 4 representing the functions with a peak in the beginning and cluster 3 covering the highest shares of above ground carbon.

In total, the share of other Conifers is moderately affecting the clustering.

Figure 20: Clustered curves for scenario SSP5-RCP8.5 and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 20: Clustered curves for scenario SSP5-RCP8.5 and PFT other Conifers. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Clusters - Temperate Broadleaf

For the fifth and last PFT Temperate Broadleaf, let’s again take a look at the first principal components depicted in Figure 21.

Figure 21: PC 1 vs. PC 2 for Temperate Broadleaf and all four scenarios.
Figure 21: PC 1 vs. PC 2 for Temperate Broadleaf and all four scenarios.

Despite the lack of data (especially in the Control scenario), some grouping becomes apparent.

Figure 22 shows the clustering for Control. Since only a few curves are unequal to zero in each cluster, no valid interpretation is possible.

Figure 22: Clustered curves for scenario Control and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 22: Clustered curves for scenario Control and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

In comparison to Figure 22, the two warming scenarios, depicted in Figure 23 (SSP1-RCP2.6) and Figure 24 (SSP3-RCP7.0) are both dominated by one cluster covering most of the non-zero curves, namely cluster 2 and cluster 3, respectively.

Figure 23: Clustered curves for scenario SSP1-RCP2.6 and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 23: Clustered curves for scenario SSP1-RCP2.6 and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 24: Clustered curves for scenario SSP3-RCP7.0 and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 24: Clustered curves for scenario SSP3-RCP7.0 and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

Figure 25 shows the clusters for scenario SSP5-RCP8.5. Here, the data situation is better, since there is a higher share of Temperate Broadleaf in general. We can see that cluster 4 reflects the grid cells with a higher share of above ground carbon. Note that cluster 4 is the smallest of all clusters.

Figure 25: Clustered curves for scenario SSP5-RCP8.5 and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.
Figure 25: Clustered curves for scenario SSP5-RCP8.5 and PFT Temperate Broadleaf. The colored curves indicate the belonging to the respective cluster. The dark curves represent the cluster-specific mean functions.

In summary, the PFT Temperate Broadleaf marginally affects the clustering.

Summary

To conclude and bring together all the results, here, the effects of the PFTs on the clusters are summarized for each scenario.

Control:

SSP1-RCP2.6:

SSP3-RCP7.0:

SSP5-RCP8.5:

In total, the clusters are especially influenced by PFTs Needleleaf Evergreen, Pioneering Broadleaf and other Conifers.